What, then, remains for us?  Is it not this—­the acquisition of knowledge, the cultivation of virtue and of friendship, the observance of faith and truth, an unrepining submission to whatever befalls us, a life led in accordance with reason?

Platonism in the museum.  But, though the Alexandrian Museum was especially intended for the cultivation of the Aristotelian philosophy, it must not be supposed that other systems were excluded.  Platonism was not only carried to its full development, but in the end it supplanted Peripateticism, and through the New Academy left a permanent impress on Christianity.  The philosophical method of Plato was the inverse of that of Aristotle.  Its starting- point was universals, the very existence of which was a matter of faith, and from these it descended to particulars, or details.  Aristotle, on the contrary, rose from particulars to universals, advancing to them by inductions.

Plato, therefore, trusted to the imagination, Aristotle to reason.  The former descended from the decomposition of a primitive idea into particulars, the latter united particulars into a general conception.  Hence the method of Plato was capable of quickly producing what seemed to be splendid, though in reality unsubstantial results; that of Aristotle was more tardy in its operation, but much more solid.  It implied endless labor in the collection of facts, a tedious resort to experiment and observation, the application of demonstration.  The philosophy of Plato is a gorgeous castle in the air; that of Aristotle a solid structure, laboriously, and with many failures, founded on the solid rock.

An appeal to the imagination is much more alluring than the employment of reason.  In the intellectual decline of Alexandria, indolent methods were preferred to laborious observation and severe mental exercise.  The schools of Neo-Platonism were crowded with speculative mystics, such as Ammonius Saccas and Plotinus.  These took the place of the severe geometers of the old Museum.

Physical science in the museum.  The Alexandrian school offers the first example of that system which, in the hands of modern physicists, has led to such wonderful results.  It rejected imagination, and made its theories the expression of facts obtained by experiment and observation, aided by mathematical discussion.  It enforced the principle that the true method of studying Nature is by experimental interrogation.  The researches of Archimedes in specific gravity, and the works of Ptolemy on optics, resemble our present investigations in experimental philosophy, and stand in striking contrast with the speculative vagaries of the older writers.  Laplace says that the only observation which the history of astronomy offers us, made by the Greeks before the school of Alexandria, is that of the summer solstice of the year B.C. 432. by Meton and Euctemon.  We have, for the first time, in that school, a combined system of observations made with instruments for the measurement of angles, and calculated by trigonometrical methods.  Astronomy then took a form which subsequent ages could only perfect.